As the U.S. media and analysts sorted over the latest Twitter post from President Donald Trump about trade negotiations with China, the long-simmering Trans-Pacific Partnership trade deal went into effect over the weekend -- without either nation's involvement. 

Officially dubbed the Comprehensive and Progressive Agreement for Trans-Pacific Partnership, the trade deal among 11 nations -- including New Zealand, Canada, Vietnam and Japan -- kicked off Sunday and was cheered by New Zealand's trade minister.

"New Zealand exporters are among the first to benefit from the Comprehensive and Progressive Agreement for Trans-Pacific Partnership which takes effect today," said Hon David Parker, that nation's trade minister, in a press statement. 

Parker boasted that the deal will cut tariffs, now and in coming weeks -- with Mexico and Canada slashing tariffs Jan. 1 and Vietnam joining later in January and then Japan further reducing tariffs by April 1.

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"The CPTPP has the potential to deliver an estimated $222 million of tariff savings to New Zealand exporters annually once it is fully in force, with almost half of that - or $105 million - now available in the first 12 months," said Parker.

Japan, meanwhile, is already feeling the cut costs of imported agricultural goods coming into the world's third largest economy, according to a report from the Yomiuri Shimbun's publication, The Japan News. 

Japan -- home to Toyota Motor Corp.  (TM) - Get Report , Honda Motor Corp.  (HMC) - Get Report , Nissan Motor Corp.  (NSANY) , Subaru Corp.  (FUJHY) - Get Report  and other automakers -- is betting on increased sales of autos to the other countries in the deal, but could face trouble in agricultural exports, said the report.

Canada also expects to benefit from expanded trade, while some farm groups in the U.S. are concerned about the deal. 

Some question how far the partnership can go without cooperation from the United States, which is locked in a trade battle with China that appeared to thaw when President Trump wrote over Twitter on Saturday that he "had a long and very good call" with President Xi Jinping of China. "Deal is moving along very well. If made, it will be very comprehensive, covering all subjects, areas and points of dispute. Big progress being made!"

The two nations earlier agreed to a temporary tariff truce at least until March, putting on hold the administration's plans to raise tariffs of some $200 billion worth of Chinese imports from 10% to 25%.

Though the U.S. was originally part of the Trans-Pacific trade talks under former President Barack Obama, the proposal proved political poison by the 2016 U.S. election. 

Nonetheless, over the weekend, New Zealand, Australia, Canada, Japan, Mexico and Singapore started participating in the deal, and Vietnam will come in on Jan. 14. Later, Brunei Darussalam, Chile, Malaysia and Peru will join in.